In this paper we prove the Strong $L^p$\-stability of the heat semigroup generated by the Hodge Laplacian on complete Riemannian manifolds with non-negative Weitzenböck curvature. Based on a probabilistic representation formula, we obtain an explicit upper bound of the $L^p$\-norm of the Riesz transforms on forms on complete Riemannian manifolds with suitable curvature conditions. Moreover, we establish the Weak $L^p$\-Hodge decomposition theorem on complete Riemannian manifolds with non-negative Weitzenböck curvature.

[A correction to this paper is available.](https://doi.org/10.4171/rmi/783 )

形式上的Riesz变换和 $L（左）^{第页}$ -完备黎曼流形上的Hodge分解

李向东

摘要

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